The culture secretary, Jeremy Hunt, said on Saturday the empty seatswere "very disappointing" and suggested they could be offered to members of the public. He said the matter was being looked at "very urgently".

At Sunday's first session of the mens basketball at the 12,000 capacity basketball arena, 70% of the lower tier of seats – which includes those allocated to sponsors, Olympic officials and athletic federations – was empty. About 15% of the larger upper tier, sold to the public, was empty. In total the Guardian estimated that more than 2,000 seats were empty in the venue to watch Nigeria v Tunisia.

On Saturday, the morning swimming heats, featuring Michael Phelps and his US rival Ryan Lochte, there were an estimated 500 empty seats in one block alone. And at the morning session of the gymnastics, at which Louis Smith and the rest of the British team appeared, there were more than 1,000 empty seats despite prospective ticket buyers being told it was sold out.

Lord Coe, the chairman of the London organising committee, was dismissive of concern that too many seats were being left empty and denied that calling in the military appeared "shambolic".

When asked to identify who should have been sitting in two-and-a half empty blocks of seats at Saturday's gymnastics, Coe initially appeared to be in denial. He said: "Lets put this in perspective. Those venues are stuffed to the gunnels."

He later clarified his position saying: "We take it seriously. I don't want to see swaths of those seats empty."

"If we have the army sitting there on rest periods we can ask them if they want to sit in there and watch it," he said. "It's not mobilising the army to resolve this. I don't think there is a single person out there would thinks it is shambolic, given the way they have stepped up in the last weeks."

Coe said he believed the problem would settle down and said it was a result of representatives of national Olympic committees, sporting federations and some sponsors taking time to "work out the shape of their day" and decide where to go. The organisers said that the empty seats were predominantly left by sporting officials and claimed that sponsors were taking their seats.

Lord Moynihan, the BOA chairman, said organisers "owe it to the fans" to find a way of filling places.

"We owe it to the British sporting public to give them an opportunity to attend one of the most historic sporting events of their lives," he said.

Coe dismissed the idea of the 30-minute rule saying: "We have got a more considered way of doing that, that judges the situation on an hour by hour basis."

To fill the accredited seats the organisers must find people with existing accreditation to the venues which rules out members of the public.

Up to 150 local school children and school teachers who are already accredited to the park, under a pre-existing scheme meant to fill seats in accredited areas, will be used alongside the soldiers.

Excluding the football, between 100,000 and 120,000 Olympic ticketsremain unsold, organisers said today. Some of those are already for sale online and others are the process of being returned by sponsors and public from abroad.

A Wimbledon-style returns system, allowing people already on the Olympic Park to pick up tickets to the last parts of sessions of basketball,hockey, handball and water polo, is now in operation.

Childrens' tickets cost £1 and adult tickets cost £5. Yesterday, 280 were sold. Passes allowing people onto the park, but not into venues, remain on sale.

During the sometimes controversial ticketing process, during which 6.6m of the 8.8m tickets were made available to members of the public, organisers repeatedly highlighted the lengths they were going to make sure there were no empty seats.

They said they wanted to avoid the situation that occurred in Beijing and at other Games, where even at sessions that were officially sold out there were large areas of empty seats – particularly for morning heats.

The problem tends to be caused by IOC stipulations that retain a certain number of seats for officials, athletes, international federations and other accredited individuals. It can be particularly acute on the morning after the opening ceremony, which finished close to 1am.

In the vast majority of the venues, at least one-fifth of seats are reserved for sponsors, officials, the media and the "Olympic family".

In the most popular sessions, such as the opening ceremony and the 100m final, the proportion is closer to half.

Those thronging the park who had been unable to get into the venues to watch any live action were critical of the empty seats, which can also be highly embarrassing if shown on television.

"I think it's terrible, especially when so many people want a ticket," said Sharon Beers from Portsmouth, "there should be less seats for officials."